Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub,' Lisa sits on a tooth-throne in the tub, which has red cloth draped over the arms with gold tassels around the edge. However when Bart comes to take the tub, Lisa stands up on the throne and yells "Bart, no!" In this shot the tassels are gone. (00:17:45)
Audio problem: At the theatre, when the cook talks to Mark Hamill off-stage he sounds exactly like Moe the bartender.
Continuity mistake: When Sideshow Bob is shouting and screaming just before he is taken away in a police van, Lisa and Bart swap places right before Bart says "Take him away, boys."
Revealing mistake: When Homer is giving Marge, Lisa and Bart money, Homer puts his hand on Bart's shoulder and whispers 'Mel's movie really stinks'. When he lets go of Bart to say this, he leaves his fingers on Bart's shoulder, but he still has fingers on his hand.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
Plot hole: In the last part of the episode, when Mr Burns is trying to convince Homer on his float to play a big prank, the timing is totally wrong. Firstly, Lisa sees the writing 'Happy Pranksgiving' on the side of Mr Burns' float way before it reaches her, and it takes Mr Burns ages to change into the Father Christmas outfit.
Lisa's Rival - S6-E2
Continuity mistake: The position of Ralph's Star Wars action figures changes the two times they show his diorama.
Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
Continuity mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
Large Marge - S14-E4
Factual error: In Luigi's, the lobsters in the tank are bright red. They are actually quite dark brown until they are boiled when they become red/pink.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: During the family's breakfast, in most shots Marge sits right beside Maggie's highchair, but in certain close-ups they are quite a few feet away from one another. (00:05:25)
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: The shot glass that Burns places on his desk disappears for several frames before reappearing. (00:05:45)
Tree House of Horror XII - S13-E1
Audio problem: In Reaper Madness; the scene where Homer destroys the Grim Reaper with a bowling ball, Bart is pinned on the wall by the Reaper's scythe. The scythe disappears and Bart says "Cool!" but his mouth just opens up and doesn't match the word.
Continuity mistake: When we first see Homer feeding the can to the goat the background shows a wooden coop. In the next shot, a purple tree stump appears there too.
Continuity mistake: When Homer shows his "incriminating photos," you can see that in them, he is bald. We know from several previous episodes that Homer had hair when Bart was a baby. He even has a bit of hair when Lisa is born.
Continuity mistake: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: The bible that Reverend Lovejoy returns at the library is bigger in the first shot.
Continuity mistake: At The Town meeting Mayor Quimby's tan disappears in the middle of the scene.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the bar, before Bart stomps on Mr. Burns' foot, his back is toward Smithers, but in the next shot, his back is turned toward everyone else. (00:19:15)
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer